Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23772011 | C2 | semidirect |
| 3. #23765615 | C2 | semidirect |
| 4. #23765173 | C2 | semidirect |
| 5. C2×#19098377 | C2 | semidirect |
| 6. C79×#2115 | C2 | semidirect |
| 13. #19098612 | C22 | semidirect |
| 18. #19098386 | C22 | semidirect |
| 22. #349×C79 | C22 | semidirect |
| 136. #2115 | D79 | semidirect |
| 137. C79 | #33657 | semidirect |
| 153. #349 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773048 | 2 |
| #23772011 | 2 |
| #23765615 | 2 |
| #23765173 | 2 |
| C2×#19098377 | 2 |
| C79×#2115 | 2 |
| #33657 | 79 |